This thesis contains a collection of results in computational geometry that are inspired from music theory literature. The solutions to the problems discussed are based on a representation of musical rhythms where pulses are viewed as points equally spaced around the circumference of a circle and onsets are a subset of the pulses. All our results for rhythms apply equally well to scales, and many of the problems we explore are interesting in their own right as distance geometry problems on the circle. / In this thesis, we characterize two families of rhythms called deep and Euclidean. We describe three algorithms that generate the unique Euclidean rhythm for a given number of onsets and pulses, and show that Euclidean rhythms are formed of repeating patterns of a Euclidean rhythm with fewer onsets, followed possibly by a different rhythmic pattern. We then study the conditions under which we can transform one Euclidean rhythm to another through five different operations. In the context of measuring rhythmic similarity, we discuss the necklace alignment problem where the goal is to find rotations of two rhythms and a perfect matching between the onsets that minimizes some norm of the circular distance between the matched points. We provide o (n2)-time algorithms to this problem using each of the ℓ1, ℓ2, and ℓinfinity norms as distance measures. Finally, we give a polynomial-time solution to the labeled beltway problem where we are given the ordering of a set of points around the circumference of a circle and a labeling of all distances defined by pairs of points, and we want to construct a rhythm such that two distances with a common onset as endpoint have the same length if and only if they have the same label.

This thesis studies measures of musical rhythm complexity. Informally, rhythm complexity may be thought of as the difficulty humans have performing a rhythm, listening to a rhythm, or recognizing its structure. The problem of understanding rhythm complexity has been studied in musicology and psychology, but there are approaches for its measurement from a variety of domains. This thesis aims to evaluate rhythm complexity measures based on how accurately they reflect human-based measures. Also, it aims to compare their performance using rhythms from Africa, India, and rhythms generated randomly. The results suggest that none of the measures accurately reflect the difficulty humans have performing or listening to rhythm; however, the measures do accurately reflect how humans recognize a rhythm's metrical structure. Additionally, the results suggest a need for normalization of the measures to account for variety among cultural rhythms.

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An attempt has been made to determine whether or not a handbook to be used by student teachers and a handbook to be used by supervising teachers would be a significant and worthwhile contribution, not only to Taylor University, but to education in general.

The present research quantified the shoulder rhythm for arm postures that represent the right-handed reachable workspace and compared 3 methods of scapular tracking: acromion marker cluster (AMC), stylus and scapular locator. The shoulder rhythm models can be incorporated into existing and future shoulder biomechanical models to determine shoulder geometry when simulating postures experienced in workplaces and thus have ergonomic implications for correctly identifying risk factors. The results of this research also provide guidance for future studies involving scapular tracking. Fourteen male and 14 female participants performed static arm postures spread over 5 elevation angles: 0, 45, 90, 135, 180 degrees, three elevation planes: 0, 45, 90 degrees to the frontal plane and, three axial rotations: maximum internal, neutral, and maximum external rotation. Kinematic data was recorded using a Vicon MX20+ motion-tracking system. Bone rotations were calculated using Euler angles and continuous prediction models were generated to estimate scapular and clavicular orientations based primarily on thoracohumeral relative orientations. Methods of scapular tracking were compared using repeated measures analysis of variance. Participant characteristics did not influence any of the scapular or the clavicular angles (p>.05). Axial rotation did not influence scapular retraction/protraction and elevation plane did not influence clavicular elevation (p>.05). Elevation angle was the largest contributor to lateral rotation and posterior tilt of the scapula and all clavicular angles. Plane of elevation was the largest contributor to scapular protraction. Using the stylus as the gold standard, the locator and the AMC underestimated lateral rotation, with a maximum difference of 11 degrees and 9 degrees between the locator and the stylus and AMC and the stylus measurements, respectively. The AMC and the locator overestimated posterior tilt at overhead postures and underestimated it at low elevation angles. The maximum difference between the AMC- and the locator- and the stylus-measured tilt was 10 degrees. The scapular locator consistently overestimated protraction by approximately 5 degrees. The AMC underestimated protraction in the frontal plane at low elevation angle but overestimated it at all other postures and the overestimation increased with plane of elevation, internal rotation and elevation angle. Overall, it is recommended to use AMC rather than the scapular locator to measure scapular position.

MAGEL2 is one of the five genes inactivated in Prader-Willi Syndrome (PWS), a genetic disorder, manifesting with symptoms of developmental delay and morbid obesity. Magel2 is highly expressed in the suprachiasmatic nucleus, which is the location of the central clock or circadian pacemaker. Magel2 knockout mice exhibit defects in circadian rhythm. I hypothesized that Magel2 plays a role in one of the inter-connecting feedback loops that control circadian rhythm in suprachiasmatic neurons. I determined that Magel2 acts as a repressive protein in the cycles feedback loop using a luciferase assay. Magel2 exerts this effect by restricting the movement of Bmal1 into the nucleus. Magel2 levels are then reduced by increasing Per2, associated with increase movement into the nucleus, as determined by experiments examining subcellular localization and effects on protein levels. Loss of Magel2 in PWS may contribute to sleep abnormalities in this disorder, specifically the cycling between different sleep stages.

The Recurrence of Rhythm is an inquiry into the notion that the voice flows ??? a theme that continually recurs in the Homeric poems, Plato's Cratylus and James Joyce's A Portrait of the Artist as a Young Man and Ulysses. Through a re-interpretation of the meaning of rhythmos in pre-Socratic philosophy, I define rhythm as the particular manner in which the voice is flowing, and argue that it is the specific quality of phonetic writing to represent the flowing aspect of the voice. The Greek concept of rhythmos is held to be inseparable from the invention of phonetic writing and the transcription of the Homeric poems, and it is this new definition of rhythm that allows the thesis to engage in contemporary debates concerning the relationship between speech and writing (as developed by Derrida, Ong, Havelock, Parry, Lord and Prier). I also argue that the Platonic concept of rhythm qua metre provides an essential point of mediation between the Greek oral tradition and the history of Western literature, a move that sets the scene for a comparative study of Homer and Joyce. By developing an original concept of recurrence that pertains to both the repetition of themes in the Homeric poems and the heroic experience of living for the sake of the story, this thesis proposes that rhythm and recurrence are interrelated concepts that distinguish the lyrical and dramatic modes that structure the epic form of narrative found in both Homer's poems and Joyce's novels. Drawing upon the esthetic philosophy of Stephen Dedalus, I develop the dialectical theory of genre first outlined by Joyce in the Paris notebook, and argue that the latent lyricism contained in the narrative style of A Portrait is a proto-typical form of the interior monologue found in Ulysses. In opposition to the early modernist paradigm of Joyce criticism, this thesis rejects the notion that mythic archetypes function as Platonic ideals (i.e. the transcendent form of the modernist artwork), but rather holds that heroic themes recur in the mental stream of the modern subject, and manifest themselves immediately through Joyce???s use of the interior monologue technique.

The system of music education devised by Emile Jacques-Dalcroze is based on an interrelated programme which includes solfege, rhythmic movement, plastique and improvisation. Although Dalcroze wrote numerous articles discussing his methods, he failed to provide a comprehensive account of his approach to the music-learning experience. Consequently this thesis aims, by a critical survey and analysis of Dalcroze’s writings, to provide an insight into the meanings and objectives of Dalcroze Eurhythmics. In addition, this investigation will seek to reveal that Dalcroze’s teaching received direction both from a multitude of influences and his extraordinary pre-occupation with rhythm. As a music teacher, Dalcroze had endeavoured to heighten the rhythmic sensitivity of his pupils by the use of kinesthetic exercises. As an humanitarian, Dalcroze’s research into rhythmic manifestations led him to propose rhythm as a dominating force effecting the future welfare of humankind. An understanding of this theory, despite its grandiose tone, is especially relevant to achieving a fuller comprehension of Dalcroze’s musical studies.

Diss. (sammanfattning) Stockholm : Karol. inst., 2003. / Härtill 5 uppsatser.